200 / 19.30 = 10.36
Usain ran 10.36 meters per second
Answer:
V =169.56
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
V = 3.14 * (3)^2 * 6
V =169.56
Answer:
the probability that takes between 4 and 5 minutes to make the sandwich is 1/3 (33.33%)
Step-by-step explanation:
since the random variable X= time taken to make a grilled cheese sandwich is uniformly distributed, then the probability is governed by
P(a<X<b)= proportion of the time considered / total time range = (a-b)/(c-d) , where c is the maximum time and d is the minimum one
then
P(4<X<5) = (5-4)/(11-3) = 1/8 = 0.125
since we already know that takes less than 6 minutes , then
P(X<6)= P(3<X<6) = (6-3)/(11-3) = 3/8 = 0.375
then using the theorem of Bayes
P( 4<X<5 | X<6 ) = P ( 4<X<5 ∩ X<6 ) / P(X<6) = P(4<X<5)/P(3<X<6) = 0.125 /0.375 = 1/3 (33.33%)
therefore given that we already know that will take Michelle less than 6 minutes , the probability that takes between 4 and 5 minutes to make the sandwich is 1/3 (33.33%)
Just do 12 times 2 d=24 because 24 divided by 12 =2
Answer:
See explanation
Step-by-step explanation:
We have to prove the identity
![tan(\frac{\Theta }{2})=\frac{sin\Theta}{1+cos\Theta }](https://tex.z-dn.net/?f=tan%28%5Cfrac%7B%5CTheta%20%7D%7B2%7D%29%3D%5Cfrac%7Bsin%5CTheta%7D%7B1%2Bcos%5CTheta%20%7D)
We will take right hand side of the identity
![\frac{sin\Theta}{1+cos\Theta}=\frac{2sin(\frac{\Theta }{2})cos(\frac{\Theta }{2})}{1+[2cos^{2}(\frac{\Theta }{2})-1]}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%5CTheta%7D%7B1%2Bcos%5CTheta%7D%3D%5Cfrac%7B2sin%28%5Cfrac%7B%5CTheta%20%7D%7B2%7D%29cos%28%5Cfrac%7B%5CTheta%20%7D%7B2%7D%29%7D%7B1%2B%5B2cos%5E%7B2%7D%28%5Cfrac%7B%5CTheta%20%7D%7B2%7D%29-1%5D%7D)
![=\frac{2sin(\frac{\Theta }{2})cos(\frac{\Theta }{2})}{2cos^{2}(\frac{\Theta }{2})}=\frac{sin(\frac{\Theta }{2})}{cos(\frac{\Theta }{2})}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B2sin%28%5Cfrac%7B%5CTheta%20%7D%7B2%7D%29cos%28%5Cfrac%7B%5CTheta%20%7D%7B2%7D%29%7D%7B2cos%5E%7B2%7D%28%5Cfrac%7B%5CTheta%20%7D%7B2%7D%29%7D%3D%5Cfrac%7Bsin%28%5Cfrac%7B%5CTheta%20%7D%7B2%7D%29%7D%7Bcos%28%5Cfrac%7B%5CTheta%20%7D%7B2%7D%29%7D)
[ Tan θ will be positive since θ lies in 1st quadrant ]